Suppression of superradiance from an ensemble of two-level atoms in the presence of foreign gas collisions

I compute the suppression in the superradiant radiation flux from an ensemble of homogeneously-broadened two-level atoms in a slab geometry configuration due to the increase in the polarization transverse decay rate caused by decoherence due to foreign gas collisions. I show that the differences between the total width of the polarization at low excitation with the magnitude of the real part of the eigenvalues and of the dominant and leading modes of the 1-D Lienard-Wiechert kernel are the critical parameters that determine the particular regimes for the superradiant flux dependence on the collision width.